THE BIRTH OF STRING THEORY String theory is currently the best candidate for a unified theory of all forces and all forms of matter in nature. As such, it has become a focal point for physical and philosophical discussions. This unique book explores the history of the theory s early stages of development, as told by its main protagonists. The book journeys from the first version of the theory (the so-called Dual Resonance Model) in the late 1960s, as an attempt to describe the physics of strong interactions outside the framework of quantum field theory, to its reinterpretation around the mid-1970s as a quantum theory of gravity unified with the other forces, and its successive developments up to the superstring revolution in 1984. Providing important background information to current debates on the theory, this book is essential reading for students and researchers in physics, as well as for historians and philosophers of science. andrea cappelli is a Director of Research at the Istituto Nazionale di Fisica Nucleare, Florence. His research in theoretical physics deals with exact solutions of quantum field theory in low dimensions and their application to condensed matter and statistical physics. elena castellani is an Associate Professor at the Department of Philosophy, University of Florence. Her research work has focussed on such issues as symmetry, physical objects, reductionism and emergence, structuralism and realism. filippo colomo is a Researcher at the Istituto Nazionale di Fisica Nucleare, Florence. His research interests lie in integrable models in statistical mechanics and quantum field theory. paolo di vecchia is a Professor of Theoretical Physics at Nordita, Stockholm, and at the Niels Bohr Institute, Copenhagen. He has worked on several aspects of theoretical particle physics, and has contributed to the development of string theory since its birth in 1968.
THE BIRTH OF STRING THEORY Edited by ANDREA CAPPELLI INFN, Florence ELENA CASTELLANI Department of Philosophy, University of Florence FILIPPO COLOMO INFN, Florence PAOLO DI VECCHIA Nordita, Stockholm and Niels Bohr Institute, Copenhagen
cambridge university press Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo, Delhi, Mexico City Cambridge University Press The Edinburgh Building, Cambridge CB2 8RU, UK Published in the United States of America by Cambridge University Press, New York Information on this title: /9780521197908 C Cambridge University Press 2012 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2012 Printed in the United Kingdom at the University Press, Cambridge A catalogue record for this publication is available from the British Library Library of Congress Cataloguing in Publication data The birth of string theory / edited by Andrea Cappelli, INFN, Florence; Elena Castellani, Department of Philosophy, University of Florence; Filippo Colomo, INFN, Florence; Paolo Di Vecchia, Niels Bohr Institute, Copenhagen and Nordita, Stockholm. p. cm. Includes bibliographical references and index. ISBN 978-0-521-19790-8 1. String models. 2. Duality (Nuclear physics) I. Cappelli, Andrea, editor of compilation. II. Castellani, Elena, 1959 editor of compilation. III. Colomo, F., editor of compilation. IV. Di Vecchia, P. (Paolo), editor of compilation. QC794.6.S85B57 2012 539.7 258 dc23 2011052388 ISBN 978-0-521-19790-8 Hardback Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
Contents List of contributors Photographs of contributors Preface Abbreviations and acronyms page x xiv xxi xxiv Part I Overview 1 1 Introduction and synopsis 3 2 Rise and fall of the hadronic string 17 gabriele veneziano 3 Gravity, unification, and the superstring 37 john h. schwarz 4 Early string theory as a challenging case study for philosophers 63 elena castellani EARLY STRING THEORY Part II The prehistory: the analytic S-matrix 81 5 Introduction to Part II 83 5.1 Introduction 83 5.2 Perturbative quantum field theory 84 5.3 The hadron spectrum 88 5.4 S-matrix theory 91 5.5 The Veneziano amplitude 97 6 Particle theory in the Sixties: from current algebra to the Veneziano amplitude 100 marco ademollo 7 The path to the Veneziano model 116 hector r. rubinstein v
vi Contents 8 Two-component duality and strings 122 peter g.o. freund 9 Note on the prehistory of string theory 129 murray gell-mann Part III The Dual Resonance Model 133 10 Introduction to Part III 135 10.1 Introduction 135 10.2 N-point dual scattering amplitudes 137 10.3 Conformal symmetry 145 10.4 Operator formalism 147 10.5 Physical states 150 10.6 The tachyon 153 11 From the S-matrix to string theory 156 paolo di vecchia 12 Reminiscence on the birth of string theory 179 joel a. shapiro 13 Personal recollections 191 daniele amati 14 Early string theory at Fermilab and Rutgers 193 louis clavelli 15 Dual amplitudes in higher dimensions: a personal view 198 claud lovelace 16 Personal recollections on dual models 202 renato musto 17 Remembering the supergroup collaboration 208 francesco nicodemi 18 The 3-Reggeon vertex 214 stefano sciuto Part IV The string 219 19 Introduction to Part IV 221 19.1 Introduction 221 19.2 The vibrating string 223 19.3 The rotating rod 226 19.4 The relativistic point particle 228
Contents vii 19.5 The string action 230 19.6 The quantum theory of the string 231 20 From dual models to relativistic strings 236 peter goddard 21 The first string theory: personal recollections 262 leonard susskind 22 The string picture of the Veneziano model 266 holger b. nielsen 23 From the S-matrix to string theory 275 yoichiro nambu 24 The analogue model for string amplitudes 283 david b. fairlie 25 Factorization in dual models and functional integration in string theory 294 stanley mandelstam 26 The hadronic origins of string theory 312 richard c. brower TOWARDS MODERN STRING THEORY Part V Beyond the bosonic string 329 27 Introduction to Part V 331 27.1 Introduction 331 27.2 Chan Paton factors 333 27.3 The Lovelace Shapiro amplitude 334 27.4 The Ramond model 335 27.5 The Neveu Schwarz model 338 27.6 The Ramond Neveu Schwarz model 339 27.7 World-sheet supersymmetry 341 27.8 Affine Lie algebras 344 28 From dual fermion to superstring 346 david i. olive 29 Dual model with fermions: memoirs of an early string theorist 361 pierre ramond 30 Personal recollections 373 andré neveu 31 Aspects of fermionic dual models 378 edward corrigan
viii Contents 32 The dual quark models 393 korkut bardakci and martin b. halpern 33 Remembering the dawn of relativistic strings 407 jean-loup gervais 34 Early string theory in Cambridge: personal recollections 414 claus montonen Part VI The superstring 419 35 Introduction to Part VI 421 35.1 Introduction 421 35.2 The field theory limit 423 35.3 Unification of all interactions 427 35.4 The QCD string 431 35.5 A detour on spinors 433 35.6 Spacetime supersymmetry 434 35.7 The GSO projection 437 35.8 The Kaluza Klein reduction and supersymmetry breaking 439 35.9 The local supersymmetric action for the superstring 442 35.10 Supergravity 444 36 Supersymmetry in string theory 447 ferdinando gliozzi 37 Gravity from strings: personal reminiscences of early developments 459 tamiaki yoneya 38 From the Nambu Goto to the σ -model action 474 lars brink 39 Locally supersymmetric action for the superstring 484 paolo di vecchia 40 Personal recollections 490 eugène cremmer 41 The scientific contributions of Joël Scherk 496 john h. schwarz Part VII Preparing the string renaissance 509 42 Introduction to Part VII 511 42.1 Introduction 511 42.2 Supergravity unification of all interactions 512 42.3 A novel light-cone formalism 514 42.4 Modern covariant quantization 518
Contents ix 42.5 Anomaly cancellation 521 42.6 A new era starts or, maybe better, continues 525 43 From strings to superstrings: a personal perspective 527 michael b. green 44 Quarks, strings and beyond 544 alexander m. polyakov 45 The rise of superstring theory 552 andrea cappelli and filippo colomo Appendix A Theoretical tools of the Sixties 569 Appendix B The Veneziano amplitude 579 Appendix C From the string action to the Dual Resonance Model 586 Appendix D World-sheet and target-space supersymmetry 604 Appendix E The field theory limit 620 Index 626
Contributors Marco Ademollo Dipartimento di Fisica, Università di Firenze, and INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Daniele Amati SISSA, Trieste, and INFN, Sezione di Trieste, via Bonomea 265, 34136 Trieste, Italy Korkut Bardakci Department of Physics, University of California, and Theoretical Physics Group, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA Lars Brink Department of Fundamental Physics, Chalmers University of Technology, S-412 96 Göteborg, Sweden Richard C. Brower Physics Department, Boston University, 590 Commonwealth Avenue, Boston, MA 02215, USA Andrea Cappelli INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Elena Castellani Dipartimento di Filosofia, Università di Firenze, Via Bolognese 52, 50139 Firenze, Italy Louis Clavelli Department of Physics and Astronomy, University of Alabama, Tuscaloosa, AL 35487-0324, USA x
List of contributors xi Filippo Colomo INFN, Sezione di Firenze, Via G. Sansone 1, 50019 Sesto Fiorentino (FI), Italy Edward Corrigan Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK Eugène Cremmer Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France Paolo Di Vecchia Niels Bohr Institute, Blegdamsvej 17, 2100 Copenhagen, Denmark, and Nordita, Roslagstullsbacken 23, 10691 Stockholm, Sweden David B. Fairlie Department of Mathematical Sciences, Durham University, Durham, DH1 3LE, UK Peter G. O. Freund Enrico Fermi Institute and Department of Physics, University of Chicago, 5720 S. Ellis Avenue, Chicago, IL 60637, USA Murray Gell-Mann Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA Jean-Loup Gervais Laboratoire de Physique Théorique, École Normale Supérieure, 24 rue Lhomond, 75231 Paris Cedex 05, France Ferdinando Gliozzi Dipartimento di Fisica Teorica, Università di Torino, and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy Peter Goddard Institute for Advanced Study, Olden Lane, Princeton, NJ 08540, USA Michael B. Green DAMTP, Wilberforce Road, Cambridge, CB3 0WD, UK Martin B. Halpern Department of Physics, University of California, and Theoretical Physics Group, Lawrence Berkeley National Laboratory, University of California, Berkeley, CA 94720, USA
xii List of contributors Claud Lovelace Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA Stanley Mandelstam Department of Physics, University of California, and Lawrence Berkeley Laboratory, University of California, Berkeley, CA 94720, USA Claus Montonen Department of Physics, University of Helsinki, P.O. Box 64, 00014 Helsinki, Finland Renato Musto Dipartimento di Scienze Fisiche, Università di Napoli Federico II, and INFN, Sezione di Napoli, 80126, Napoli, Italy Yoichiro Nambu Department of Physics, University of Chicago, 5720 S. Ellis Avenue, Chicago, IL 60637, USA André Neveu Laboratoire de Physique Théorique et Astroparticules, Case 070, CNRS, Université Montpellier II, 34095 Montpellier, France Francesco Nicodemi Dipartimento di Scienze Fisiche, Università di Napoli Federico II, and INFN, Sezione di Napoli, 80126, Napoli, Italy Holger B. Nielsen Niels Bohr Institute, Blegdamsvej 17, 2100, Copenhagen, Denmark David I. Olive Department of Physics, Swansea University, Singleton Park, Swansea, SA2 8PP, UK Alexander M. Polyakov Joseph Henry Laboratories, Princeton University, Princeton, NJ 08544, USA Pierre Ramond Institute for Fundamental Theory, Physics Department, University of Florida, Gainesville, FL 32611, USA Hector R. Rubinstein AlbaNova University Center, Royal Institute of Technology, Stockholm University, 106 91 Stockholm, Sweden
List of contributors xiii John H. Schwarz Department of Physics, Mathematics and Astronomy, California Institute of Technology, 456 Lauritsen Laboratory Caltech 452-48, Pasadena, CA 91125, USA Stefano Sciuto Dipartimento di Fisica Teorica, Università di Torino, and INFN, Sezione di Torino, Via P. Giuria 1, 10125 Torino, Italy Joel A. Shapiro Department of Physics and Astronomy, Rutgers University, 136 Frelinghuysen Road, Piscataway, NJ 08854-8019, USA Leonard Susskind Department of Physics, Stanford University, Stanford, CA 94305-4060, USA Gabriele Veneziano Theory Division, CERN, CH-1211 Geneva 23, Switzerland, and Collège de France, 11 place M. Berthelot, 75005 Paris, France Tamiaki Yoneya Institute of Physics, University of Tokyo, Komaba, Meguro-ku, Tokyo 153-8902, Japan
Photographs of contributors From left to right and from top to bottom: Marco Ademollo, Daniele Amati, Korkut Bardakci, Lars Brink, Richard C. Brower and Louis Clavelli. xiv
Photographs of contributors xv From left to right and from top to bottom: Edward Corrigan, Eugène Cremmer, Paolo Di Vecchia, David B. Fairlie, Peter G. O. Freund, Sergio Fubini (1928 2005), Murray Gell-Mann, Jean-Loup Gervais and Ferdinando Gliozzi.
xvi Photographs of contributors From left to right and from top to bottom: Peter Goddard, Michael B. Green, Martin B. Halpern, Claud Lovelace, Stanley Mandelstam, Claus Montonen, Renato Musto, Yoichiro Nambu and André Neveu [photograph of Goddard by Cliff Moore].
Photographs of contributors xvii From left to right and from top to bottom: Francesco Nicodemi, Holger B. Nielsen, David I. Olive, Alexander M. Polyakov, Pierre Ramond, Hector R. Rubinstein (1933 2009), Bunji Sakita (1930 2002), Joël Scherk (1946 1980) and John H. Schwarz.
xviii Photographs of contributors From left to right and from top to bottom: Stefano Sciuto, Joel A. Shapiro, Leonard Susskind, Gabriele Veneziano and Tamiaki Yoneya.
Participants at the meeting The Birth of String Theory, 18 19 May 2007, GGI, Arcetri, Florence.
Preface In May 2007 we organized a workshop on the origin and early developments of string theory at the Galileo Galilei Institute for Theoretical Physics in Arcetri (Florence). A fair number of researchers who had contributed to the birth of the theory participated and described, according to their personal recollections, the intriguing way in which the theory developed from hadron phenomenology into an independent field of research. It was the first occasion on which they had all been brought together since the 1975 conference in Durham, which represented the last meeting on string theory as applied to hadronic physics. The workshop in Arcetri was a success: the atmosphere was enthusiastic and the participants showed genuine pleasure in discussing the lines of thought developed during the years from the late Sixties to the beginning of the Eighties, mutually checking their own reminiscences. This encouraged us to go on with the project we had been thinking of for some time, of an historical account of the early stages of string theory based on the recollections of its main exponents. We were fortunate enough to have on board practically all the physicists who developed the theory. While some of the contributions to this Volume originated from the talks presented at the meeting, most of them have been written expressly for this book. In starting this project we were motivated by the observation that the history of the beginnings and early phases of string theory is not well accounted for: apart from the original papers, the available literature is rather limited and fragmentary. A book devoted specifically to the historical reconstruction of these developments the formulation of a consistent and beautiful theory starting from hadron phenomenology, its failure as a theory of strong interactions, and, finally, its renaissance as a unified theory of all fundamental interactions was not available. This Volume aims to fill the gap, by offering a collection of reminiscences and overviews, each one contributing from the Author s own perspective to the general historical account. The collection is complemented with an extended editorial apparatus (Introductions, Appendices and Editors Chapters) according to criteria explained below. In addition to the historical record, this book is of interest for several reasons. First, by showing the dynamics of the ideas, concepts and methods involved, it offers precious background information for a better understanding of the present status of string theory, xxi
xxii Preface which has recently been at the centre of a widespread debate. Second, it provides an illustration of the fruitfulness of the field, from both a physical and a mathematical perspective. A number of ideas that are central to contemporary theoretical physics of fundamental interactions, such as supersymmetry and extra spacetime dimensions, originated in this context. Furthermore, some theoretical methods, for example two-dimensional conformal symmetry, found important physical applications in various domains outside the original one. Finally, from a philosophical point of view, early string theory represents a particularly interesting case study for reflections on the construction and evaluation of physical theories in modern physics. In the following, we illustrate the structure of the book and offer some guidelines to the reader. The Volume is organized into seven Parts: the first one provides an overview of the whole book; the others correspond to significant stages in the evolution of string theory from 1968 to 1984 and are accompanied by specific introductory Chapters. In Part I, the Introduction summarizes the main developments and contains a temporal synopsis with a list of key results and publications. The following two Chapters, by Veneziano and by Schwarz, offer a rather broad overview on the early (1968 1973) and later (1974 1984) periods of the history of string theory, respectively. They introduce all the themes of the book that are then addressed in detail in the following Parts. The last Chapter of Part I, by Castellani, presents some elements for the philosophical discussion of the early evolution of the theory and the scientific methodology employed in it. The Introductions to the other Parts and the Appendices are meant to fit the needs of undergraduate/early graduate students in theoretical physics, as well as of historians and philosophers, who have a background in quantum mechanics and quantum field theory, but lack the specific vocabulary to appreciate fully the Authors contributions. The Introductions and Appendices, taken together with the final Chapter, can also be used as an entry-level course in string theory, presenting the main physical ideas with a minimum of technique. For a broader audience, we suggest beginning with the first, nontechnical paragraph in each Introduction, and then approaching the less technical and more comprehensive Authors Chapters which are located first in each Part. The rich material presented in the Chapters, together with the original literature, can be the starting point for in-depth historical study of the many events that took place in the development of string theory. The final Chapter of the book, by Cappelli and Colomo, provides a nontechnical overview of string theory from 1984 up to the present time, which complements the historical and scientific perspective. We hope that the book can be read at different levels and, as such, will be useful for scientific, historical and philosophical approaches to this fascinating, but complex, subject. The book has associated the webpage http://theory.fi.infn.it/colomo/string-book/ which gives access to the original talks of the 2007 GGI workshop and to additional material already provided by some Authors or to be collected in the future.
Preface xxiii We are very grateful to all those who have helped us in preparing this Volume. First and foremost, our thanks go to all the Authors who agreed to contribute their reminiscences. Many thanks go also to all those who gave us valuable comments and suggestions during the preparation of the Volume, in particular Leonardo Castellani, Camillo Imbimbo, Yuri Makeenko, Raffaele Marotta, Giulio Peruzzi, Igor Pesando, Franco Pezzella, Augusto Sagnotti, John H. Schwarz, Domenico Seminara, Gabriele Veneziano, Guillermo R. Zemba and Hans v. Zur-Mühlen. We are indebted to the Galileo Galilei Institute for hosting the 2007 workshop. We also wish to thank the staff of Cambridge University Press for assistance and Sara De Sanctis for helping with the bibliography. Finally, we are grateful to our collaborators and to our families for their patience and support.
Abbreviations and acronyms AdS AdS/CFT APS BRST Caltech CERN CFT CNRS CP CPT DAMTP DDF DHS Dp-brane DRM ENS Fermilab FESR FNAL GGI GGRT GR GSO GUT IAS ICTP IHES IMF INFN IR ISR Anti de Sitter (spacetime) Anti de Sitter/conformal field theory (correspondence) American Physical Society Becchi Rouet Stora Tyutin (quantization) California Institute of Technology, Pasadena, CA European Centre for Nuclear Research, Geneva conformal field theory Centre National de la Recherche Scientifique, France Chan Paton (factors) charge conjugation, parity, time reversal (symmetries) Department of Applied Mathematics and Theoretical Physics, Cambridge Del Giudice Di Vecchia Fubini (states, operators) Dolen Horn Schmid (duality) Dirichlet p-dimensional membrane Dual Resonance Model École Normale Supérieure, Paris Fermi National Accelerator Laboratory (or FNAL), Illinois finite energy sum rule Fermi National Accelerator Laboratory (or Fermilab), Illinois Galileo Galilei Institute, Florence Goddard Goldstone Rebbi Thorn (quantization) general relativity Gliozzi Scherk Olive (projection) Grand Unified Theories Institute of Advanced Study, Princeton, NJ International Center for Theoretical Physics, Trieste Institut des Hautes Études Scientifiques, Bures-sur-Yvette infinite momentum frame Istituto Nazionale di Fisica Nucleare, Italy infrared Intersecting Storage Ring, CERN xxiv
Abbreviations and acronyms xxv ITP KK KM KN KZ LEP LHC LPTENS LPTHE MIT MSSM M-theory NAL NATO Nordita NS NSF NYU PCAC PS QCD QED QFT R RIMS RNS SISSA SLAC S-matrix SM SSC SSR SUGRA SUSY SVM TOE UV WZ WZWN YM (Kavli) Institute of Theoretical Physics, Santa Barbara, CA Kaluza Klein (compactification) Kac Moody (algebra) Koba Nielsen (amplitudes) Knizhnik Zamolodchikov (equation) Large Electron Positron (collider), CERN Large Hadron Collider, CERN Laboratoire de Physique Théorique, École Normale Supérieure, Paris Laboratoire de Physique Théorique et Hautes Energies, Orsay Massachusetts Institute of Technology, Boston, MA Minimal Supersymmetric Standard Model matrix (or membrane) theory National Accelerator Laboratory (FNAL after 1972), Illinois North Atlantic Treaty Organization Nordic Institute for Theoretical Physics, Stockholm Neveu Schwarz (model, sector) National Science Foundation, USA New York University partially conserved axial current Proton Synchrotron, CERN quantum chromodynamics quantum electrodynamics quantum field theory Ramond (model, sector) Research Institute for Mathematical Sciences, Kyoto Ramond Neveu Schwarz (model) Scuola Internazionale Superiore di Studi Avanzati, Trieste Stanford Linear Accelerator Center scattering matrix Standard Model Superconducting Super Collider superconvergence sum rule supergravity supersymmetry Shapiro Virasoro model Theory of Everything ultraviolet Wess Zumino (model) Wess Zumino Witten Novikov (model) Yang Mills (gauge theory)